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      <title>IM1- Unit 2- Linear and Exponential Relationships by Erica Campos</title>
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      <pubDate>2017-07-16 00:55:19 UTC</pubDate>
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         <title>Standards</title>
         <author>camposroom104</author>
         <link>https://padlet.com/camposroom104/IM1unit2/wish/178771677</link>
         <description><![CDATA[<div>PRIORITY:<br>A.REI.12​ Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear<br>inequalities in two variables as the intersection of the corresponding half-planes.<br><br>F.IF.2​ Use function notation, evaluate functions for inputs in their domains, and interpret<br>statements that use function notation in terms of a context.<br><br>F.IF.6 ​Calculate and interpret the average rate of change of a function (presented symbolically<br>or as a table) over a specified interval. Estimate the rate of change from a graph.★<br><br>F.IF.7​ Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★<br>a. Graph linear and quadratic functions and show intercepts, maxima, and minima.<br>e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and<br>trigonometric functions, showing period, midline, and amplitude.<br><br>F.BF.1​ Write a function that describes a relationship between two quantities.★<br>a. Determine an explicit expression, a recursive process, or steps for calculation from a context.<br>b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.<br><br>F.LE.1​ Distinguish between situations that can be modeled with linear functions and with<br>exponential functions.<br>a. Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.<br>b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.<br>c. Recognize situations in which a quantity grows or decays by a constant percent rate<br>per unit interval relative to another.<br><br>F.LE.2​ Construct linear and exponential functions, including arithmetic and geometric<br>sequences, given a graph, a description of a relationship, or two input-output pairs (include<br>reading these from a table).<br><br>SUPPORTING:<br>A.REI.10​ Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).<br><br>F.IF.1​ Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the<br>equation y = f(x).<br><br>F.IF.3​ Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for .<br><br>F.IF.4​ For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive,<br>or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★<br><br>F.IF.5​ Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★<br><br>F.IF.9​ Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an<br>algebraic expression for another, say which has the larger maximum.<br><br>F.BF.2​ Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★<br><br>F.BF.3​ Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from<br>their graphs and algebraic expressions for them.<br><br>F.LE.3​ Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.<br><br>F.LE.5​ Interpret the parameters in a linear or exponential function in terms of a context.</div>]]></description>
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         <pubDate>2017-07-16 01:30:07 UTC</pubDate>
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         <title>Learning Objectives</title>
         <author>camposroom104</author>
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         <description><![CDATA[<ul><li>Students will identify all key parts of functions and evaluate functions.</li><li>Students will interpret linear functions in context.</li><li>Students will graph linear functions and interpret their graphs from parent functions.</li><li>Students will calculate and interpret the average rate of change of a function over a specified interval.</li><li>Students will create linear functions from linear models, understanding the rate of change in the situation.</li><li>Students will compare two linear functions from linear models and interpret their solution.</li><li>Students will graph linear inequalities and interpret their solution on the coordinate plane and also in<br>context.</li><li>Students will graph exponential functions, understand key features: asymptote, vertical shift, and the relationship to parent functions.</li><li>Students will discover that geometric sequences are exponential functions.</li><li>Students will solve exponential growth and decay functions from real world situations.</li><li>Students will construct arithmetic and geometric sequences and write the rules.</li></ul>]]></description>
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         <pubDate>2017-07-16 01:30:22 UTC</pubDate>
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         <title>Essential Questions</title>
         <author>camposroom104</author>
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         <description><![CDATA[<ul><li>How can I use key features to describe relationships between different functions?</li><li>How do I graph linear functions and identify key<br>features?</li><li>How can a graph be interpreted in context of the<br>situation?</li><li>How does graphing a linear inequality compare to graphing a linear equation?</li><li>How are exponential functions used in real life<br>situations?</li></ul>]]></description>
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         <pubDate>2017-07-16 01:30:33 UTC</pubDate>
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         <title>Tier 2</title>
         <author>camposroom104</author>
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         <description><![CDATA[<div>Notation<br>Model<br>Notation<br>Investment<br>Principal<br>Interest<br>Rate<br>Depreciation (decay)<br>Per<br>Appreciation&nbsp; (growth)</div>]]></description>
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         <pubDate>2017-07-18 06:50:59 UTC</pubDate>
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         <title>Tier 3</title>
         <author>camposroom104</author>
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         <description><![CDATA[<div>Function<br>Linear<br>Value<br>Equation<br>Evaluate<br>Table<br>Input<br>Output<br>Domain<br>Range<br>Graph<br>Relationship<br>Constant Rate of Change (slope) Sets<br>Subsets<br>Integers<br>Increase<br>Decrease<br>Term&nbsp;<br>Rule<br>Constant Function<br>Common Ratio<br>Rate<br>Evaluate<br>Table<br>Input<br>Output<br>Graph<br>Relationship<br>Data<br>Increase<br>Decrease<br>Term<br>Rule<br>Constant Function<br>Geometric Sequence<br>Arithmetic Sequence<br>Graph<br>Relationship Data<br>Curve<br>Exponential Function<br>Exponent<br>Increase<br>Decrease<br>Growth Factor<br>Term<br>Finite Sequence<br>Infinite Sequence<br>Rule (function/equation)</div>]]></description>
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         <pubDate>2017-07-18 06:51:06 UTC</pubDate>
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         <pubDate>2017-10-07 21:42:19 UTC</pubDate>
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         <pubDate>2017-10-13 20:55:23 UTC</pubDate>
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         <pubDate>2017-10-13 20:55:48 UTC</pubDate>
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         <pubDate>2017-11-03 03:17:54 UTC</pubDate>
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         <pubDate>2017-11-03 03:26:44 UTC</pubDate>
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         <pubDate>2018-11-05 17:59:06 UTC</pubDate>
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         <pubDate>2018-11-05 17:59:51 UTC</pubDate>
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         <pubDate>2019-10-20 15:45:33 UTC</pubDate>
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         <pubDate>2019-10-20 16:23:42 UTC</pubDate>
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